STD: A Seasonal-Trend-Dispersion Decomposition of Time Series

TL;DR

This paper introduces a novel seasonal-trend-dispersion (STD) decomposition method for time series that captures trend, seasonal patterns, and variance, addressing heteroscedasticity often neglected by existing methods, and enhances analysis and forecasting.

Contribution

The paper presents the first decomposition method that explicitly models time series variance alongside trend and seasonal components, improving understanding and forecasting accuracy.

Findings

STD effectively captures heteroscedasticity in time series.

The method improves forecasting by incorporating dispersion analysis.

STD provides a comprehensive view of time series components.

Abstract

The decomposition of a time series is an essential task that helps to understand its very nature. It facilitates the analysis and forecasting of complex time series expressing various hidden components such as the trend, seasonal components, cyclic components and irregular fluctuations. Therefore, it is crucial in many fields for forecasting and decision processes. In recent years, many methods of time series decomposition have been developed, which extract and reveal different time series properties. Unfortunately, they neglect a very important property, i.e. time series variance. To deal with heteroscedasticity in time series, the method proposed in this work -- a seasonal-trend-dispersion decomposition (STD) -- extracts the trend, seasonal component and component related to the dispersion of the time series. We define STD decomposition in two ways: with and without an irregular component. We show how STD can be used for time series analysis and forecasting.